Find $\lim_{x\to -3}\dfrac{-5}{(x+3)^2}$. Choose 1 answer: Choose 1 answer: (Choice A) A $0$ (Choice B) B $-\dfrac{5}{36}$ (Choice C) C $-\dfrac{5}{6}$ (Choice D) D The limit doesn't exist
Solution: Let's try to find the limit using direct substitution. $\begin{aligned} \lim_{x\to -3}\dfrac{-5}{(x+3)^2}&=\dfrac{-5}{(-3+3)^2} \\\\ &=\dfrac{-5}{0} \end{aligned}$ Our expression evaluates to a nonzero number over zero. In such cases, the limit doesn't exist. In conclusion, $\lim_{x\to -3}\dfrac{-5}{(x+3)^2}$ doesn't exist.